# Ambivalent not implies strongly ambivalent

From Groupprops

This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., ambivalent group) neednotsatisfy the second group property (i.e., strongly ambivalent group)

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## Statement

It is possible to have an ambivalent group (i.e., a group in which all elements are Real element (?)s) that is *not* a strongly ambivalent group. In particular, there is at least one element that is not a Strongly real element (?).

As a corollary, a real element of a group need not be a strongly real element.

## Proof

### Example of the quaternion group

`Further information: quaternion group`

The quaternion group of order eight is an ambivalent group. However, it is *not* strongly ambivalent, because the only elements of order are , and these definitely do not generate the whole group.

### Other examples

Other examples include special linear group:SL(2,5).